Question

If x=2+root3, find value of x+1/x.

Answer 1

ANSWER:---------

given x = 2 + √3

therefore 1/x = 1/(2 + √3)

= 1/(2 + √3) × (2 - √3)/(2 - √3)

= (2 - √3)/[(2 + √3)(2 - √3)

= (2 - √3)/[(2)² - (√3)²]

= (2 - √3)/(4 - 3)

= 2 - √3

the value of x = 2 - √3

hence, x + 1/x = 2 + √3 + (2 - √3)

= 2 + √3 + 2 - √3

= 4

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